this file 43 468 1 PB
OPEN ACCESS
Ind. Journal on Computing
Vol. 1, Issue. 2, Sept 2016. pp. 13-26
doi:10.21108/indojc.2016.1.2.43
ISSN 2460-9056
socj.telkomuniversity.ac.id/indojc
Implementation of Evolution Strategies for
Classifier Model Optimization
Mahmud Dwi Sulistiyo #1, Rita Rismala #2
# School of Computing, Telkom University
Jl. Telekomunikasi, Terusan Buah Batu, Bandung, Indonesia 40257
1
mahmuddwis@telkomuniversity.ac.id
2
ritaris@telkomuniversity.ac.id
Abstract
Classification becomes one of the classic problems that are often encountered in the field of artificial
intelligence and data mining. The problem in classification is how to build a classifier model through
training or learning process. Process in building the classifier model can be seen as an optimization
problem. Therefore, optimization algorithms can be used as an alternative way to generate the classifier
models. In this study, the process of learning is done by utilizing one of Evolutionary Algorithms (EAs),
namely Evolution Strategies (ES). Observation and analysis conducted on several parameters that
influence the ES, as well as how far the general classifier model used in this study solve the problem. The
experiments and analyze results show that ES is pretty good in optimizing the linear classification model
used. For Fisher’s Iris dataset, as the easiest to be classified, the test accuracy is best achieved by 94.4%;
KK Selection dataset is 84%; and for SMK Major Election datasets which is the hardest to be classified
reach only 49.2%.
Keywords: classification, optimization, classifier model, Evolutionary Algorithms, Evolution Strategies
Abstrak
Salah satu masalah klasik yang sering dijumpai dalam dunia kecerdasan buatan dan data mining
adalah klasifikasi. Permasalahan pada klasifikasi ialah bagaimana membangun model classifier melalui
proses training atau learning. Proses pembentukan model klasifikasi dapat dipandang sebagai
permasalahan optimasi. Oleh karenanya, algoritma-algoritma optimasi dapat digunakan sebagai alternatif
cara untuk menghasilkan model classifier tersebut. Pada penelitian ini, proses learning dilakukan dengan
memanfaatkan salah satu Evolutionary Algorithms (EAs), yaitu Evolution Strategies (ES). Observasi dan
analisis dilakukan terhadap beberapa parameter yang berpengaruh pada ES, serta sejauh mana model
umum classifier yang digunakan pada penelitian ini. Dari percobaan dan analisis yang telah dilakukan, ES
cukup baik dalam melakukan optimasi pada model klasifikasi linear yang digunakan. Untuk dataset
Fisher’s Iris yang paling mudah untuk diklasifikasikan, akurasi uji terbaik yang dicapai adalah sebesar
94.4%; untuk dataset Pemilihan KK sebesar 84%; dan untuk dataset Jurusan SMK yang paling sulit untuk
diklasifikasikan mencapai 49.2%.
Kata Kunci: klasifikasi, optimasi, model classifier, Evolutionary Algorithms, Evolution Strategies
Received on August 2016. Accepted on Sept 2016
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
14
I. INTRODUCTION
Data classification is a classic problem often encountered in the world of artificial intelligence and data
mining. In some cases, computer requires the ability of classification, as instance to recognize certain patterns,
to predict a value on the specific issues of space, even to decide something or build a recommendation
system.
Generally, there are two concepts in solving the problem of classification, namely memory-based and
model-based classification. On the concept of memory-based, the ability to classify an input specified by the
data history has ever had before. Pattern of the history data that best matches the input data is the basis to
determine the class results. The concept is certainly very inflexible because it is very dependent on the
availability and completeness of data. In addition, it needs large data capacity to store the history data which
will be continuously increasing. Therefore, the model-based concept was commonly used instead of memorybased one.
By model-based classification, the history data is still needed, but only on the training phase, which refers
to the classifier model building process. Once the training phase is completed, the history data (training data)
is not needed and the system simply uses the classifier model, resulted from the training phase, to classify
new input data. Various methods to train and generate the model classifier have been applied. They are like
the use of Distant Supervision for Twitter sentiment classification [4], Artificial Neural Network in brain
tumor detection and classification [10], as well as the use of Data Mining technique for student college
enrollment approval [15]. However, a study for the optimization remains to be done since the ability of the
classifier system cannot be generalized to all problems. It depends on the conditions of data involved.
Basically, the phase of training or learning is a process to produce the optimal configuration of the
classifier model, given the conditions that are generally initiated at random. If it is associated with other
problems in the world of artificial intelligence, the classifier model building process can be seen as an
optimization problem. Therefore, optimization algorithms can also be used as an alternative way to generate a
classifier model on classification problems. So far, the optimization algorithm that requires minimal cost but
with optimal results in a relatively large of problem space is the optimization algorithms based on evolution
concepts or commonly called as Evolutionary Algorithms (EAs). In this study, EAs will be applied as an
alternative training method in the modeling classifier.
II. LITERATURE REVIEW
A. Previous Works
One important step in solving the problem of classification is the process of learning which is done to
build a classifier model that can map a set of attributes X to one of Y class labels that have been defined
previously [7]. Classification has been widely applied in various fields, including the field of health [11, 10],
education [15], social media [4, 14], and many others. If it is associated with problems in the world of
artificial intelligence, the development process of this classifier models can be seen as optimization problems.
In this case, the aim of optimization process is to minimize the classification error and finally obtain the
classifier model.
Evolutionary Algorithms (EAs) is a meta-heuristic optimization algorithm that adapts the process of
evolution and natural selection proposed by Charles Darwin. EAs are widely used in the optimization problem
where the solution space given is very large and complex so that it can hardly be solved by using Exhaustive
Search methods since it costs a very long time. The mentioned problems are like Traveling Salesman
Problems [19], satisfiability problem [5], and Vertex Cover Problem [12]. In general, EAs have been shown
to produce a solution to problems where the search space is complex, multimodal, non-differential,
discontinuous, noisy, and time-dependent [8].
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
15
Furthermore, a study to combine EAs and Artificial Neural Network had been conducted for time series
prediction [17]. The study utilized Evolution Strategies (ES), one of EAs, to be an alternative method in the
ANN training phase. The purpose was to obtain optimal weights for all neuron connections. Based on the
experiments conducted, in the testing results, the error yielded by ES algorithm was tend to be better than the
Back Propagation, a typical algorithm to train ANN. Therefore, the study concluded that ES algorithm was
applicable as an alternative solution (substituting BP algorithm) in the learning process of the ANN. In
addition, it is possible to use other prediction models [17].
B. Evolution Strategies
In this paper, one of EAs will be applied as a proposed method is Evolution Strategies.
BEGIN
INITIALIZE population with
random candidate solutions;
EVALUATE each candidate;
REPEAT UNTIL (TERMINATION
CONDITION is satisfied) DO
1 SELECT parents;
2 RECOMBINE pairs of parents;
3 MUTATE the resulting offspring;
4 EVALUATE new candidates;
5 SELECT individuals for the next generation;
END
Pseudo-code 1. Evolutionary Algorithms [3]
Evolution Strategies (ES) was initially built to solve a simple parameter optimization problem. But, in the
development, ES nowadays has been applied widely to deal with various problems which are more complex,
like image processing and computer vision [9], scheduling [6], automatic system [13], and time series
prediction [16]. The main characteristics of ES compared to other EAs can be found in the chromosome
representation and the evolution operator type [2].
ES chromosome is represented as a real number which consists of three parts, namely object variable ,
strategy parameter of mutation step size , and strategy parameter of rotation angle . However, not all of
them should be exist in an ES chromosome [3]. The chromosome representations used in this study are
scheme 1 and scheme 2 which are
and
respectively. Note that the
and
symbols are used as brackets for representing chromosome contents.
In addition, the main evolution operator used in ES is mutation [1]. The process of mutation in ES is done
by adding a random number generated using normal distribution. The mutation operator is performed to
whole parts of chromosome, where the mutation for should be done first before it is done for . This
operator is applied for each chromosome that belongs to parent population. Basically, only successful or
better resulted chromsome is kept for next generations. Technically, the process of mutation in ES depends on
the chromosome scheme used. Table 1 shows mutation processes for chromosome with scheme 1 and 2 which
are used in this study.
Table 1. Mutation process using scheme 1 and 2 on ES chromosome [3]
Mutation for scheme 1: without correlation and with one
• Chromosome form
• x1,…,xn, , consisting object variables xi and one gen of
mutation step size
• Mutation for
• ’ = . exp( . N(0,1))
• Mutated chromosome
• x’i = xi + ’ . N(0,1)
• Learning rate
• is the learning rate and usually set to be near to 1/n½
• Boundary rule
• There is a boundary rule for ’, if ’ < 0 then ’ = 0
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
16
Mutation for scheme 2: without correlation and with n number of
• Chromosome form
• x1,…,xn, 1,…, n , consisting object variables xi and n
gens of mutation step sizes
• Mutation for
• ’i = i . exp(’ . N(0,1) + . Ni (0,1))
• Mutated chromosome
• x’i = xi + ’i . Ni (0,1)
• Learning rate
• There are 2 parameters of learning rate:
- is learning rate for all genes, set to be near to 1/(2n)½
- ’ is learning rate for each gene, set to be near to 1/(2n½)½
• Boundary rule
• There is a boundary rule for ’, if ’ < 0 then ’ = 0
This unique mutation mechanism makes ES having a property of Self-adaptation, which is the ability to
adapt the optimum value which probably changes all over the time by determining strategy parameters
adaptively during the searching process. Along with mutation as the main operator, ES also has an addition
operator namely recombination or some references call it as crossover. Recombination in ES is also applied
for parent population, until gaining predetermined number of new chromosomes. The number of child
chromosome targeted is influenced by a parameter called as selective pressure. Each recombination process
done in ES produces only one child chromosome from two parent chromosomes.
There are two mechanisms in generating each gene for a child chromosome, namely (1) Intermediate:
average value of a pair gene values of two parent chromosomes; or (2) Discrete: choosing one of two gene
values from two parent chromosomes in the same index. Besides, there are two common ways as well in
determining the two chromsomes as parent to produce one child chromosome, namely (1) Local: it uses only
2 chromosomes which is selected unchangedly for all child genes; or (2) Global: for every child gene, it uses
different pair of parent chromsomes (generates n pairs for n child genes). As the result, there are 4 method
combinations to perform recombination in ES as shown in Table 2 [18].
Table 2. Recombination methods in ES
Method
zi = (xi + yi)/2
One fixed pair of
chromosomes
Local Intermediate
n pairs of chromosomes for
n genes
Global Intermediate
zi = xi or yi chosen randomly
Local Discrete
Global Discrete
Note: z is child, while x and y are parent
Meanwhile, survivor selection is performed after gaining number of child chromosomes resulted by
both mutation and recombination process of
number of parent chromosomes. Generally, the survivor
selection is done by selecting number of chromosomes having best fitness among others. The selecting way
can be performed to 2 alternatives, namely ( + )-selection (union of parent and child chromosomes) or ( , )selection (only child chromosomes will be involved) [18].
Overall main properties of ES can be viewed in the Table 3 below [1].
Table 3. Main properties of Evolution Strategies
Chromosome representation
Parent selection
Mutation
Recombination / crossover
Survivor selection
Unique feature
Real values
Uniform distribution; using Local or Global
As main evolution operator; using Gaussian
perturbation
As additional evolution operator; using
Discrete or Intermediate
or
Self-adaptation in the strategy parameters
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
17
III. RESEARCH METHOD
This research methodology consists of the following activities.
1. Literature study, a study of the literature related to the classification, evolutionary algorithms, as well as
materials that will support this research.
2. Data collecting, a phase of collecting all the data required by the system, both for pre-research, as well as
for the core of the study itself.
3. Designing the system, a stage where system is being designed, starting from the data design to analyzing
the system architecture.
4. Implementation, which includes data preprocessing, feature extraction, classifier model development, and
testing the system.
5. Experiment and analysis, a stage where the system is being tested to measure and analyze the system
performance, including accuracy and processing time.
6. Writing report, documentation and reporting are needed for every observation and experiment results
Literature
Study
Collecting
Data
Designing
System
Writing
Report
Experiment
and Analysis
System
Implementation
Figure 1. Activities in the research methodology
In the Collecting Data, there are 3 kinds of data used, namely Fisher’s Iris, SMK (equal to Senior High
School) Major Election, dan Field Interest (KK) Selection dataset.
Fisher’s Iris is a dataset which is commonly used in many studies of machine learning and building
classifier model. This dataset has domain of real values and is linearly separable in term of classification, so
that it is very suitable to use as a simple case study here. The total number of records in this dataset is 150, in
which 100 records are for train set and the rest is for test set.
Table 4. Attribute of Fisher’s Iris dataset
Attribute
Sepal length
Sepal width
Petal length
Petal width
Class (Species)
Value
Real [4 .. 8]
Real [2 .. 5]
Real [1 .. 7]
Real [0 .. 3]
Setosa = 1, Versicolor = 2, Virginica = 3
SMK Major Election contains students’ junior high school examination marks who will enter the SMK.
Target for each input data pattern is the designated major among three options, namely Software Engineering
(RPL), Multimedia, and Computer Engineering & Networks (TKJ). SMK Major Election dataset can also be
used to train a classifier model for a majors recommendation system. In general, the characteristics of this
dataset is non-linearly separable. Moreover, actually in determining the major, there are some subjective
considerations to be involved.
This dataset consists of:
-
Input: The National Examination (UN), the Examination Schools (US), and the Final Value (NA)
Target: Majors (RPL, Multimedia, TKJ)
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
-
18
Considering that NA is a combination value between UN and US with a particular weighting and to
reduce the dimensionality of the data, the selected attribute for input is NA.
The number of records for the train set is 209, while for the test set is 90.
Table 5. Attribute of SMK Major Election dataset
Attribute (NA)
Indonesian
English
Math
Science
Major
Value
Real [0 .. 10]
Real [0 .. 10]
Real [0 .. 10]
Real [0 .. 10]
RPL = 1, Multimedia = 2, TKJ = 3
KK Selection dataset contains the courses marks taken by the students, along with the choice of each
student's KK. The source of the data in this study were derived from Bachelor degree of Informatics
Engineering, Telkom University. Basically, the values obtained by each student can be considered to choose
which KK is suitable for him. There are 3 KKs used as the study case here: ICM (Intelligence, Computing and
Multimedia), SIDE (Software Engineering, Information Systems, and Data Engineering), and TELE
(Telematics). The number of records for the train set is 308, while for the test set is 131.
Indeed, not all the students always pay attention to their academic ability to determine the designated KK
because there are particular personal reasons as well. However, selecting KK by students at the Telkom
University also involves guardian lecturer or faculty trustee who will provide input and direction by looking
at their academic potential. Therefore, the dataset for KK selection here belongs to a non-linearly separable
dataset. The input of the raw data consists of marks of the courses that students have taken, that are already
converted from letters into numbers. Then, those values are grouped (being averaged) into several groups of
KK subjects corresponding to the course curriculum. Meanwhile the target data is the selected KK for each
student having corresponding courses marks.
Table 6. Attribute of KK Selection dataset
Attribute
Compulsory subjects
ICM subjects
SIDE subjects
TELE subjects
Lab courses
Selected KK
Value
Real [0 .. 4]
Real [0 .. 4]
Real [0 .. 4]
Real [0 .. 4]
Real [0 .. 4]
ICM = 1, SIDE = 2, TELE = 3
The general process flow in the system is started with input data that has been previously pre-processed.
The data is the train set, which is a set of records used to build the classifier model. Next, the process goes to
run training phase, the process of forming and optimizing the model, so that a classifier model is obtained.
The trained model then be tested to see the performance or ability in classifying test data that had not been
processed before.
Here is a general view of the classification system development in this study.
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
START
Test
set
Train
set
19
Training using
ES algorithm
Testing
Classifier
model
Classification
results
FINISH
Figure 2. General overview of the classification system development using ES
The general form of the model classifier used in this study is a linear equation. Each input feature in the
data is multiplied by a weight, then the product of each pair of input and weight will be totaled. The set of
weight values is here said to be the classifier model. Results obtained by multiplying the number of inputs and
the weights will determine the level of eligibility to be classified to a particular class. The weights given for
one class are different with the weights given to other classes, but still with the same input. The output class is
determined by finding the highest value among these three values of eligibility.
The purpose of the model building process here is to find the right values for all weight multipliers to be
able to classify patterns of input data into classes in accordance with the best possible accuracy. Formulas (1)
to (4) show the classifier models used in this study.
{
(1)
(2)
(3)
(4)
where:
: eligibility to be classified to
: eligibility to be classified to
: eligibility to be classified to
: input values of the data
: weights for input 1 to to get the eligibility for
: weights for input 1 to to get the eligibility for
: weights for input 1 to to get the eligibility for
Figure 3 depicts the ES algorithm or scheme used in this study.
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
20
Mutation
Initiation
Population
Recombination
No
Termination?
New
Population
Survivor
Selection
Yes
End
Fitness
Mutated Chromosome + Offspring
Start
Decode &
Evaluation
Figure 3. Scheme or algorithm of ES
As described in the Literature Review section, here are some technical guides to perform ES algorithm.
1.
2.
3.
4.
Mutation process performed using the mutation step size. This explains that there is a limitation when
each individual will move or mutate from the original position. Thus, the evolutionary process becomes
more focused.
Recombination process has several choices of methods, namely Discrete or Intermediate in determining
the child genes, as well as Global or Local in the parent selection process.
ES has a selective pressure parameter that indicates one chromosome will be compared to a number of
chromosomes before being chosen as the best one and will survive in the next generation.
The process of recombination and mutation can be done in parallel, so the execution order is regardless.
Chromosomes that have been decoded was evaluated using the fitness formula which is defined as
follows.
(5)
Notes:
= the number of data records that is classified correctly
= the number of data records that is involved in training phase
In this study, a chromosome in ES represents the weighting multiplier values of each input feature data.
Input values on train set are multiplied by the weights to yield the eligibility value for admission to each class,
the class 1 to class n, where n is the number of classes on the data involved. By using the formula (1), the
output class will be obtained for each input pattern. Fitness value is obtained by calculating the percentage
level of accuracy between output and target class that has been given.
IV. RESULTS AND DISCUSSION
During the experiment, training phase through an evolution process and testing phase to see the
performance of the classifier model that had been trained, was conducted using the test set. The purpose of
this experiment was to analyze the influence of some parameter values on the evolutionary process and result.
In addition, the observations were also done to obtain optimal combination of the parameter values, including
population size, selective pressure, and recombination method.
For each experiment and observation, the specified maximum generation was 50 and it used ( , )selection as the survivor selection method. There were two conditions as the criteria of the evolution
termination. First, if it had met the predefined maximum generation and the second one was if the best fitness
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
21
did not change in a number of consecutive generations. Each observation was applied to 3 datasets that have
been prepared, the Fisher's Iris, SMK Major Election, and KK Selection.
As the information on each resulted table to be analyzed, scheme = chromosome scheme; popOrtu = the
size of the parent population; selPres = selective pressure; selOrtu = method of parent selection; hitGen =
how to calculate the child's genes; accTr = average accuracy rate of train set (%); accTs = average accuracy
rate of test set (%); and Wkt = average processing time (seconds).
A. Observing the Size of Parent Population
In the first stage of ES observation, there was no information related to the values of the parameters that
should be used. Therefore, the determined values were commonly set. The selective pressure was 7, while the
Global Discrete method was used in the recombination process.
Table 7. Observation results of the influence of parent population size to the system performance
Parameter
Scheme popOrtu
1
5
1
10
1
20
1
50
2
5
2
10
2
20
2
50
accTr
79.7
88.3
90.7
95.7
85
92.6
97.1
97.9
Iris
accTs
78.4
82.2
88.6
92.2
83.2
87.6
92
92.4
Wkt
0.8
2.27
3.52
11.9
0.86
2.07
5.36
13.3
SMK Major
accTr accTs Wkt
60.9
49.2 1.34
61.3
47
2.72
61.5
47.4
6.6
61.8
47.7 17.9
60.7
48.9 1.24
61.2
46.7 2.11
61.2
48.2
4.5
61.4
47.2 11.8
KK Selection
accTr accTs Wkt
71.9
69.8 2.28
74.8
72.3 4.49
75.8
78
9.65
75.1
74.3
21
66.8
66.6
1.7
70.4
69.8 4.78
78.8
75.8 16.1
81
77.6 42.9
The data in the table above is then simplified and resummed to obtain the average values for accuracy
rate and processing time resulted by given parent population size values. Accuracy level demonstrates the
ability of the model to classify the data, either on the train or test. Meanwhile, the processing time shows the
speed of the ES searching process to reach convergent condition. In that condition the best-so-far solution is
saturated or not changed anymore.
Table 8. The overall results from observation of parent population size
popOrtu
Acc (%)
Wkt (s)
5
68.4
1.37
10
71.2
3.08
20
74.6
7.62
50
75.4
19.8
Figure 4. Charts of the influence of the parent population to the ES performance for both the accuracy level and processing time
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
22
Based on the overall observation results table and chart above, it appears that in terms of accuracy, the
greater the parent population size are used, the ES searching process will produce a better solution models.
The size of the population describes the number of chromosomes that is evaluated by ES in every generation.
Among chromosomes in the population, the best chromosome is obtained for each generation. The larger the
population, the greater the chance of ES to get a better solution. In this experiment, it shows that the value of
50 produces the best accuracy rate. Although this rate is still very possible to go up if the population size is
increased, a value of 50 will be used as the size of the population in the next observation. It also considers that
the accuracy improvement of 20 to 50 is not too high, so as expected, if the size is increased, the accuracy
improvement would not be too big as well.
While in terms of processing time, it is clear that the larger the population size, the longer processing
time will be taken because of more chromosomes that must be evaluated. This is certainly something to be
’paid’ if the population size is increased. The computational cost is also be considered, so it is not required to
use more than 50.
B. Observation to the Selective Pressure
In the second stage of ES observation, the size of parent population used is 50, as the best result from
previous observation. Meanwhile, the Global Discrete was still used as default method in the recombination
process.
Table 9. Observation results of the influence of selective pressure to the system performance
Parameter
Scheme selPres
1
1
1
2
1
3
1
4
1
5
1
6
1
7
2
1
2
2
2
3
2
4
2
5
2
6
2
7
accTr
73.6
80.1
90.3
87.1
89.9
95.5
92.4
75.3
83.7
93.8
96.6
97.3
97.4
97
Iris
accTs
70
71
85.6
80.8
88
92.8
89
65.4
75.8
89.4
93.6
92.6
93.2
92.8
Wkt
1.93
3.21
4.01
5.83
7.34
9.64
8.77
2.22
4.08
5.34
6.88
10.7
11.5
12
SMK Major
accTr accTs Wkt
60.7
49.2 3.25
61
48.4
4.8
61.2
48.4 7.75
61.3
48.2 10.7
61.7
46.3 17.8
61.3
47.7 12.8
61.6
47.3 18.3
60.9
48.9 3.41
61.1
48.8 5.24
61.3
47.9 8.08
61.1
48.6 9.14
61.7
47.4
12
61.5
48.2 13.2
61.4
48.6 14.6
KK Selection
accTr accTs Wkt
66.1
66.3
7.7
69.3
68.4 12.8
71.9
73.1
18
74.2
74.1 20.8
75.6
75.4 29.7
74.2
73.9 24.5
77
75.4 37.6
64.1
62.9 7.41
67.9
66.6 12.7
73.2
72
16.3
77.5
76.9 27.9
78.2
74
29.4
78.1
77.4 45.8
80.6
79.7 41.6
The data in the table above is then simplified and resummed to obtain the average values for accuracy
rate and processing time resulted by given selective pressure values.
Table 10. The overall results from observation of selective pressure
selPres
Acc (%)
Wkt (s)
1
64
4.3
2
67
7.1
3
72
10
4
73
14
5
74
18
6
75
20
7
75
22
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
23
Figure 5. Charts of the influence of the selective pressure to the ES performance for both the accuracy level and processing time
Selective pressure can describe the number of chromosomes that must be countered by a particular
chromosome to be chosen as the best chromosome. For instance, if the selective pressure is set to 5, then for
every group that contains (5 + 1) chromosomes taken randomly, a chromosome will be chosen as the best one
to be maintained for the next generation. The amount of selective pressure on the ES will directly affect the
designated number of new chromosomes that are generated through mutation and recombination operation.
Similar to previous observations, in terms of the level of accuracy that is produced, with the increasing
number of new chromosomes are generated, the chance of ES to get better chromosomes is getting greater as
well. ES searching process is also becoming more exploratory with more and more widespread the candidate
solution is evaluated. In the first chart, it can be seen that when the value of selective pressure is increased
from 1 to 6, the accuracy rates of the resulted models are continued to rise. However, when it was closed to 7,
the resulted accuracy differences becomes not too far away, even almost the same. It means that the condition
at that point have already started converging, so if the value of the selective pressure continues to be added,
the accuracy may not be much different.
While on the other hand, the greater the value of selective pressure, the greater the computing time
required. It is already quite clear since with more new chromosomes that must be evaluated, ES needs longer
computational cost as well. With accuracy rates that is started to reach convergent condition, while processing
time will continue to be increased, so that 7 is chosen as the optimal selective pressure in this experiment and
will be used for the next observation.
C. Observation to the Recombination Method
This observation uses fixed values for several parameters obtained from previous observations. The
parent population size is 50 and the selective pressure is 7. These values are used in hopes of getting the best
result as well in this observation.
Table 11. Observation results of the influence of recombination method to the system performance
Scheme
1
1
1
1
2
2
2
2
Parameter
selOrtu hitGen
1
1
1
2
2
1
2
2
1
1
1
2
2
1
2
2
accTr
90.2
98.9
96.6
93.4
94.5
98.7
95.5
98.2
Iris
accTs
83.6
93.8
93.6
90.8
92
94.4
92.2
93.8
Wkt
7.47
10.2
9.57
10.2
11.3
10.8
10.1
13.2
SMK Major
accTr accTs Wkt
60.8
49.2 10.5
62.3
46.8 21.5
61.8
46.2 14.6
61.3
47.6
15
61.2
47.1 12.3
61.7
47.8 14.9
61.5
48.2 29.3
61.5
47.2 15.2
KK Selection
accTr accTs Wkt
66.1
64.7 14.3
87
84
42.3
77.6
76
21.9
74.9
75.4
25
72.9
70.2 22.8
80.2
77.9 29.6
74.8
73.7 20.4
84.5
80.5 37.1
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
24
The data in the table above is then simplified and resummed to obtain the average values for accuracy
rate and processing time resulted by given method combinations of parent selection and calculating child’s
genes.
Table 12. The overall results from observation of recombination method
selOrtu|hitGen
Acc (%)
Wkt (s)
11
71
4.74
12
77.8
8.33
21
74.8
13.1
22
75.8
19.9
Figure 6. Charts of the influence of the recombination method to the ES performance for both the accuracy level and processing time
Based on the overall observation results table and chart above, it shows that the computational cost of
searching process done by ES is very influenced by the recombination method used. It indicates that each
recombination method has its own algorithm complexity. On the second chart, it appears that the combination
of local intermediate method has the lowest complexity, while recombination with a combination of discrete
global method has the highest complexity.
By selecting the parent chromosomes locally, ES only needed to find a pair of chromosomes to produce
one new chromosome. While using global method, the pair of chromosomes to collect was as much as the
number of genes on the chromosome. Meanwhile, the process of calculating the intermediate genes was
carried only by calculating the mean between each pair of corresponding genes from both parent
chromosomes. This could be done in a single process count. In contrast to the discrete method, in which for
each pair of corresponding genes, ES had to choose which one would be taken for the child's gene. Thus, the
process would be repeated as many times as the number of genes.
On the other hand, in terms of accuracy, the combination of discrete local method showed the best result
among other combinations. By choosing parents locally, ES became more focused on the pair of
chromosomes. Thus, the searching space was smaller, which was just on the two chromosomes. Meanwhile
by the global method, the searching space was getting larger, which consisted of n pairs of parent
chromosomes. It would be more possibly to get a worse chromosome. Besides, good chromosomes basically
came from good parent chromosomes as well. However, this condition would be difficult to achieve if the
selection was done globally, where the child chromosomes were resulted by mix of many pairs of parents.
When a good chromosome was chosen as a parent, good genes from the chromosome will be ’damaged’ by
other worse chromosomes that are also selected as parents.
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
25
Meanwhile, calculations using discrete method (x|2) looks better than the intermediate (x|1). It can be
seen from the first chart that the combination of 1|2 is better than the 1|1 and 2|2 better than 2|1. Basically,
discrete method takes gene values that are already exist in the parent chromosomes. While the intermediate
method calculates parent’s genes to produce new genes with new values. So, a child generated by discrete
method is combination of values that exist in the parent chromosomes, whereas a child generated by
intermediate method always has new values.
Based on the processes that occur, intermediate method tends to be faster in achieving optimum points.
However, that is what makes the method getting more quickly and more likely to encounter premature
convergence because it is stuck in a local optimum conditions. Meanwhile, the discrete method relatively
longer to achieve optimum points. But, that feature makes ES avoids premature convergence in a local
optimum point, so that the results are truly the best. In addition, based on table 7, 9, and 11, it can be seen that
the results of the classification on Iris dataset is the most excellent among the three datasets were used. While
the SMK Major Election dataset is the most difficult to be classified. This is caused by the Iris dataset that is
linearly separable, so it will be easier to be classified by the basic model that belongs to linear classifier.
Table 13. Best accuracies of the models resulted by ES for the three datasets
Accuracy
Train (%)
Test (%)
Fisher’s Iris
98.9
94.4
SMK Major
62.3
49.2
KK Selection
87
84
The SMK Major Election dataset that produces the lowest accuracy showed that the data pattern is the
most non-linearly separable among the three datasets. It certainly makes the linear classifier model used in
this study getting difficult to classify the data pattern. Thus, the low accuracy rate resulted from the
experiment is not due to ES that is not capable of searching the solution, but the general classifier model that
is less able to cope with the complexity of a given problem. This can be resolved by using a non-linear
classification model in the next study.
V. CONCLUSION AND FUTURE WORK
Based on experiments that have been conducted, it can be concluded that ES is good enough in
optimizing the linear classifier model. ES has several unique attributes and features that are beneficial in the
searching process. In ES, the parameters of population size, selective pressure, and recombination method
used affect the results obtained from the evolutionary process, both in terms of the accuracy rate and the
processing time. Based on overall observations made, the optimal values for those three parameters are
respectively 50, 7, and discrete local. For Fisher's Iris dataset, the most easily to be classified, the best testing
accuracy rate achieved is 94.4%, while for KK Selection is 84%, and for SMK Major Election datasets as the
hardest to reach is 49.2%. Those different results occurred by influence of the linearity of the data distribution
as well as the data dimension. The more linear, the data is getting easier to be classified. Meanwhile, if the
size of the data is getting bigger, commonly it is more difficult to be classified.
As for development purposes of the future works, it is necessary to use a classifier model that is more
complex and can handle various conditions of data distribution, both linearly separable and non-linearly
separable. In addition, it can also be compared with other methods of Evolutionary Algorithms or Swarm
Intelligence based optimization method for the training phase.
ACKNOWLEDGMENT
The authors would like to thank the funding bodies of this research provided by Directorate of Research
and Community Service (DP2M), Telkom University, in The Internal Research Grant Program 2015.
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
26
REFERENCES
[1] Bäck, T., & Schwefel, H. P. (1993). An Overview of Evolutionary Algorithms for Parameter Optimization. Evolutionary Computation,
1(1), 1-23.
[2] Dianati, M., Song, I., & Treiber, M. (2002). An Introduction to Genetic Algorithms and Evolution Strategies. Technical report,
University of Waterloo, Ontario, N2L 3G1, Canada.
[3] Eiben, A. E., & Smith, J. E. (2003). Introduction to Evolutionary Computing. Springer Science & Business Media.
[4] Go, A., Bhayani, R., & Huang, L. (2009). Twitter Sentiment Classification Using Distant Supervision. CS224N Project Report,
Stanford, 1, 12.
[5] Gottlieb, J., Marchiori, E., & Rossi, C. (2002). Evolutionary Algorithms for the Satisfiability Problem. Evolutionary Computation,
10(1), 35-50.
[6] Greenwood, G. W., Gupta, A. K., & McSweeney, K. (1994, June). Scheduling Tasks in Multiprocessor Systems Using Evolutionary
Strategies. In International Conference on Evolutionary Computation (pp. 345-349).
[7] Hermawati, Fajar Astuti. (2013). Data Mining. Penerbit Andi.
[8] Jones, G. (1998). Genetic and Evolutionary Algorithms. Encyclopedia of Computational Chemistry.
[9] Louchet, J. (2000). Stereo Analysis Using Individual Evolution Strategy. In Pattern Recognition, 2000. Proceedings. 15th
International Conference on (Vol. 1, pp. 908-911). IEEE.
[10] Muhammad, L., Dayawati, R. N., & Rismala, R. (2014). Brain Tumor Detection and Classification In Magnetic Resonance Imaging
(MRI) using Region Growing, Fuzzy Symmetric Measure, and Artificial Neural Network and Connected Component Labeling.
International Journal on Information and Communication Technology| IJoICT, 1(1).
[11] Nguyen, Danh V., and David M. Rocke. "Tumor classification by partial least squares using microarray gene expression data."
Bioinformatics 18.1 (2002): 39-50.
[12] Oliveto, P. S., He, J., & Yao, X. (2007, September). Evolutionary Algorithms and the Vertex Cover Problem. In Evolutionary
Computation, 2007. CEC 2007. IEEE Congress on (pp. 1870-1877). IEEE.
[13] Ostertag, M., & Kiencke, U. (1995, September). Optimization of Airbag Release Algorithms Using Evolutionary Strategies. In
Control Applications, 1995., Proceedings of the 4th IEEE Conference on (pp. 275-280). IEEE.
[14] Pennacchiotti, M., & Popescu, A. M. (2011). A Machine Learning Approach to Twitter User Classification. ICWSM, 11, 281-288.
[15] Ragab, A. H. M., Noaman, A. Y., Al-Ghamdi, A. S., & Madbouly, A. I. (2014, June). A Comparative Analysis of Classification
Algorithms for Students College Enrollment Approval Using Data Mining. In Proceedings of the 2014 Workshop on Interaction Design
in Educational Environments (p. 106). ACM.
[16] Rismala, R. (2015). Prediksi Time Series Tingkat Inflasi Indonesia Menggunakan Evolution Strategies. Jurnal Ilmiah Teknologi
Informasi Terapan, 1(2).
[17] Sulistiyo, Mahmud Dwi, Dayawati, R. N., Nurlasmaya. (2013, November). Evolution Strategies for Weight Optimization of Artificial
Neural Network in Time Series Prediction. In Robotics, Biomimetics, and Intelligent Computational Systems (ROBIONETICS), 2013
IEEE International Conference on (pp. 143-147). IEEE.
[18] Suyanto, ST., MSc. (2008). Evolutionary Computation: Komputasi Berbasis “Evolusi” dan “Genetika”. Informatika.
[19] Tsai, H. K., Yang, J. M., Tsai, Y. F., & Kao, C. Y. (2004). An Evolutionary Algorithm for Large Traveling Salesman Problems.
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 34(4), 1718-1729.
Ind. Journal on Computing
Vol. 1, Issue. 2, Sept 2016. pp. 13-26
doi:10.21108/indojc.2016.1.2.43
ISSN 2460-9056
socj.telkomuniversity.ac.id/indojc
Implementation of Evolution Strategies for
Classifier Model Optimization
Mahmud Dwi Sulistiyo #1, Rita Rismala #2
# School of Computing, Telkom University
Jl. Telekomunikasi, Terusan Buah Batu, Bandung, Indonesia 40257
1
mahmuddwis@telkomuniversity.ac.id
2
ritaris@telkomuniversity.ac.id
Abstract
Classification becomes one of the classic problems that are often encountered in the field of artificial
intelligence and data mining. The problem in classification is how to build a classifier model through
training or learning process. Process in building the classifier model can be seen as an optimization
problem. Therefore, optimization algorithms can be used as an alternative way to generate the classifier
models. In this study, the process of learning is done by utilizing one of Evolutionary Algorithms (EAs),
namely Evolution Strategies (ES). Observation and analysis conducted on several parameters that
influence the ES, as well as how far the general classifier model used in this study solve the problem. The
experiments and analyze results show that ES is pretty good in optimizing the linear classification model
used. For Fisher’s Iris dataset, as the easiest to be classified, the test accuracy is best achieved by 94.4%;
KK Selection dataset is 84%; and for SMK Major Election datasets which is the hardest to be classified
reach only 49.2%.
Keywords: classification, optimization, classifier model, Evolutionary Algorithms, Evolution Strategies
Abstrak
Salah satu masalah klasik yang sering dijumpai dalam dunia kecerdasan buatan dan data mining
adalah klasifikasi. Permasalahan pada klasifikasi ialah bagaimana membangun model classifier melalui
proses training atau learning. Proses pembentukan model klasifikasi dapat dipandang sebagai
permasalahan optimasi. Oleh karenanya, algoritma-algoritma optimasi dapat digunakan sebagai alternatif
cara untuk menghasilkan model classifier tersebut. Pada penelitian ini, proses learning dilakukan dengan
memanfaatkan salah satu Evolutionary Algorithms (EAs), yaitu Evolution Strategies (ES). Observasi dan
analisis dilakukan terhadap beberapa parameter yang berpengaruh pada ES, serta sejauh mana model
umum classifier yang digunakan pada penelitian ini. Dari percobaan dan analisis yang telah dilakukan, ES
cukup baik dalam melakukan optimasi pada model klasifikasi linear yang digunakan. Untuk dataset
Fisher’s Iris yang paling mudah untuk diklasifikasikan, akurasi uji terbaik yang dicapai adalah sebesar
94.4%; untuk dataset Pemilihan KK sebesar 84%; dan untuk dataset Jurusan SMK yang paling sulit untuk
diklasifikasikan mencapai 49.2%.
Kata Kunci: klasifikasi, optimasi, model classifier, Evolutionary Algorithms, Evolution Strategies
Received on August 2016. Accepted on Sept 2016
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
14
I. INTRODUCTION
Data classification is a classic problem often encountered in the world of artificial intelligence and data
mining. In some cases, computer requires the ability of classification, as instance to recognize certain patterns,
to predict a value on the specific issues of space, even to decide something or build a recommendation
system.
Generally, there are two concepts in solving the problem of classification, namely memory-based and
model-based classification. On the concept of memory-based, the ability to classify an input specified by the
data history has ever had before. Pattern of the history data that best matches the input data is the basis to
determine the class results. The concept is certainly very inflexible because it is very dependent on the
availability and completeness of data. In addition, it needs large data capacity to store the history data which
will be continuously increasing. Therefore, the model-based concept was commonly used instead of memorybased one.
By model-based classification, the history data is still needed, but only on the training phase, which refers
to the classifier model building process. Once the training phase is completed, the history data (training data)
is not needed and the system simply uses the classifier model, resulted from the training phase, to classify
new input data. Various methods to train and generate the model classifier have been applied. They are like
the use of Distant Supervision for Twitter sentiment classification [4], Artificial Neural Network in brain
tumor detection and classification [10], as well as the use of Data Mining technique for student college
enrollment approval [15]. However, a study for the optimization remains to be done since the ability of the
classifier system cannot be generalized to all problems. It depends on the conditions of data involved.
Basically, the phase of training or learning is a process to produce the optimal configuration of the
classifier model, given the conditions that are generally initiated at random. If it is associated with other
problems in the world of artificial intelligence, the classifier model building process can be seen as an
optimization problem. Therefore, optimization algorithms can also be used as an alternative way to generate a
classifier model on classification problems. So far, the optimization algorithm that requires minimal cost but
with optimal results in a relatively large of problem space is the optimization algorithms based on evolution
concepts or commonly called as Evolutionary Algorithms (EAs). In this study, EAs will be applied as an
alternative training method in the modeling classifier.
II. LITERATURE REVIEW
A. Previous Works
One important step in solving the problem of classification is the process of learning which is done to
build a classifier model that can map a set of attributes X to one of Y class labels that have been defined
previously [7]. Classification has been widely applied in various fields, including the field of health [11, 10],
education [15], social media [4, 14], and many others. If it is associated with problems in the world of
artificial intelligence, the development process of this classifier models can be seen as optimization problems.
In this case, the aim of optimization process is to minimize the classification error and finally obtain the
classifier model.
Evolutionary Algorithms (EAs) is a meta-heuristic optimization algorithm that adapts the process of
evolution and natural selection proposed by Charles Darwin. EAs are widely used in the optimization problem
where the solution space given is very large and complex so that it can hardly be solved by using Exhaustive
Search methods since it costs a very long time. The mentioned problems are like Traveling Salesman
Problems [19], satisfiability problem [5], and Vertex Cover Problem [12]. In general, EAs have been shown
to produce a solution to problems where the search space is complex, multimodal, non-differential,
discontinuous, noisy, and time-dependent [8].
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
15
Furthermore, a study to combine EAs and Artificial Neural Network had been conducted for time series
prediction [17]. The study utilized Evolution Strategies (ES), one of EAs, to be an alternative method in the
ANN training phase. The purpose was to obtain optimal weights for all neuron connections. Based on the
experiments conducted, in the testing results, the error yielded by ES algorithm was tend to be better than the
Back Propagation, a typical algorithm to train ANN. Therefore, the study concluded that ES algorithm was
applicable as an alternative solution (substituting BP algorithm) in the learning process of the ANN. In
addition, it is possible to use other prediction models [17].
B. Evolution Strategies
In this paper, one of EAs will be applied as a proposed method is Evolution Strategies.
BEGIN
INITIALIZE population with
random candidate solutions;
EVALUATE each candidate;
REPEAT UNTIL (TERMINATION
CONDITION is satisfied) DO
1 SELECT parents;
2 RECOMBINE pairs of parents;
3 MUTATE the resulting offspring;
4 EVALUATE new candidates;
5 SELECT individuals for the next generation;
END
Pseudo-code 1. Evolutionary Algorithms [3]
Evolution Strategies (ES) was initially built to solve a simple parameter optimization problem. But, in the
development, ES nowadays has been applied widely to deal with various problems which are more complex,
like image processing and computer vision [9], scheduling [6], automatic system [13], and time series
prediction [16]. The main characteristics of ES compared to other EAs can be found in the chromosome
representation and the evolution operator type [2].
ES chromosome is represented as a real number which consists of three parts, namely object variable ,
strategy parameter of mutation step size , and strategy parameter of rotation angle . However, not all of
them should be exist in an ES chromosome [3]. The chromosome representations used in this study are
scheme 1 and scheme 2 which are
and
respectively. Note that the
and
symbols are used as brackets for representing chromosome contents.
In addition, the main evolution operator used in ES is mutation [1]. The process of mutation in ES is done
by adding a random number generated using normal distribution. The mutation operator is performed to
whole parts of chromosome, where the mutation for should be done first before it is done for . This
operator is applied for each chromosome that belongs to parent population. Basically, only successful or
better resulted chromsome is kept for next generations. Technically, the process of mutation in ES depends on
the chromosome scheme used. Table 1 shows mutation processes for chromosome with scheme 1 and 2 which
are used in this study.
Table 1. Mutation process using scheme 1 and 2 on ES chromosome [3]
Mutation for scheme 1: without correlation and with one
• Chromosome form
• x1,…,xn, , consisting object variables xi and one gen of
mutation step size
• Mutation for
• ’ = . exp( . N(0,1))
• Mutated chromosome
• x’i = xi + ’ . N(0,1)
• Learning rate
• is the learning rate and usually set to be near to 1/n½
• Boundary rule
• There is a boundary rule for ’, if ’ < 0 then ’ = 0
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
16
Mutation for scheme 2: without correlation and with n number of
• Chromosome form
• x1,…,xn, 1,…, n , consisting object variables xi and n
gens of mutation step sizes
• Mutation for
• ’i = i . exp(’ . N(0,1) + . Ni (0,1))
• Mutated chromosome
• x’i = xi + ’i . Ni (0,1)
• Learning rate
• There are 2 parameters of learning rate:
- is learning rate for all genes, set to be near to 1/(2n)½
- ’ is learning rate for each gene, set to be near to 1/(2n½)½
• Boundary rule
• There is a boundary rule for ’, if ’ < 0 then ’ = 0
This unique mutation mechanism makes ES having a property of Self-adaptation, which is the ability to
adapt the optimum value which probably changes all over the time by determining strategy parameters
adaptively during the searching process. Along with mutation as the main operator, ES also has an addition
operator namely recombination or some references call it as crossover. Recombination in ES is also applied
for parent population, until gaining predetermined number of new chromosomes. The number of child
chromosome targeted is influenced by a parameter called as selective pressure. Each recombination process
done in ES produces only one child chromosome from two parent chromosomes.
There are two mechanisms in generating each gene for a child chromosome, namely (1) Intermediate:
average value of a pair gene values of two parent chromosomes; or (2) Discrete: choosing one of two gene
values from two parent chromosomes in the same index. Besides, there are two common ways as well in
determining the two chromsomes as parent to produce one child chromosome, namely (1) Local: it uses only
2 chromosomes which is selected unchangedly for all child genes; or (2) Global: for every child gene, it uses
different pair of parent chromsomes (generates n pairs for n child genes). As the result, there are 4 method
combinations to perform recombination in ES as shown in Table 2 [18].
Table 2. Recombination methods in ES
Method
zi = (xi + yi)/2
One fixed pair of
chromosomes
Local Intermediate
n pairs of chromosomes for
n genes
Global Intermediate
zi = xi or yi chosen randomly
Local Discrete
Global Discrete
Note: z is child, while x and y are parent
Meanwhile, survivor selection is performed after gaining number of child chromosomes resulted by
both mutation and recombination process of
number of parent chromosomes. Generally, the survivor
selection is done by selecting number of chromosomes having best fitness among others. The selecting way
can be performed to 2 alternatives, namely ( + )-selection (union of parent and child chromosomes) or ( , )selection (only child chromosomes will be involved) [18].
Overall main properties of ES can be viewed in the Table 3 below [1].
Table 3. Main properties of Evolution Strategies
Chromosome representation
Parent selection
Mutation
Recombination / crossover
Survivor selection
Unique feature
Real values
Uniform distribution; using Local or Global
As main evolution operator; using Gaussian
perturbation
As additional evolution operator; using
Discrete or Intermediate
or
Self-adaptation in the strategy parameters
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
17
III. RESEARCH METHOD
This research methodology consists of the following activities.
1. Literature study, a study of the literature related to the classification, evolutionary algorithms, as well as
materials that will support this research.
2. Data collecting, a phase of collecting all the data required by the system, both for pre-research, as well as
for the core of the study itself.
3. Designing the system, a stage where system is being designed, starting from the data design to analyzing
the system architecture.
4. Implementation, which includes data preprocessing, feature extraction, classifier model development, and
testing the system.
5. Experiment and analysis, a stage where the system is being tested to measure and analyze the system
performance, including accuracy and processing time.
6. Writing report, documentation and reporting are needed for every observation and experiment results
Literature
Study
Collecting
Data
Designing
System
Writing
Report
Experiment
and Analysis
System
Implementation
Figure 1. Activities in the research methodology
In the Collecting Data, there are 3 kinds of data used, namely Fisher’s Iris, SMK (equal to Senior High
School) Major Election, dan Field Interest (KK) Selection dataset.
Fisher’s Iris is a dataset which is commonly used in many studies of machine learning and building
classifier model. This dataset has domain of real values and is linearly separable in term of classification, so
that it is very suitable to use as a simple case study here. The total number of records in this dataset is 150, in
which 100 records are for train set and the rest is for test set.
Table 4. Attribute of Fisher’s Iris dataset
Attribute
Sepal length
Sepal width
Petal length
Petal width
Class (Species)
Value
Real [4 .. 8]
Real [2 .. 5]
Real [1 .. 7]
Real [0 .. 3]
Setosa = 1, Versicolor = 2, Virginica = 3
SMK Major Election contains students’ junior high school examination marks who will enter the SMK.
Target for each input data pattern is the designated major among three options, namely Software Engineering
(RPL), Multimedia, and Computer Engineering & Networks (TKJ). SMK Major Election dataset can also be
used to train a classifier model for a majors recommendation system. In general, the characteristics of this
dataset is non-linearly separable. Moreover, actually in determining the major, there are some subjective
considerations to be involved.
This dataset consists of:
-
Input: The National Examination (UN), the Examination Schools (US), and the Final Value (NA)
Target: Majors (RPL, Multimedia, TKJ)
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
-
18
Considering that NA is a combination value between UN and US with a particular weighting and to
reduce the dimensionality of the data, the selected attribute for input is NA.
The number of records for the train set is 209, while for the test set is 90.
Table 5. Attribute of SMK Major Election dataset
Attribute (NA)
Indonesian
English
Math
Science
Major
Value
Real [0 .. 10]
Real [0 .. 10]
Real [0 .. 10]
Real [0 .. 10]
RPL = 1, Multimedia = 2, TKJ = 3
KK Selection dataset contains the courses marks taken by the students, along with the choice of each
student's KK. The source of the data in this study were derived from Bachelor degree of Informatics
Engineering, Telkom University. Basically, the values obtained by each student can be considered to choose
which KK is suitable for him. There are 3 KKs used as the study case here: ICM (Intelligence, Computing and
Multimedia), SIDE (Software Engineering, Information Systems, and Data Engineering), and TELE
(Telematics). The number of records for the train set is 308, while for the test set is 131.
Indeed, not all the students always pay attention to their academic ability to determine the designated KK
because there are particular personal reasons as well. However, selecting KK by students at the Telkom
University also involves guardian lecturer or faculty trustee who will provide input and direction by looking
at their academic potential. Therefore, the dataset for KK selection here belongs to a non-linearly separable
dataset. The input of the raw data consists of marks of the courses that students have taken, that are already
converted from letters into numbers. Then, those values are grouped (being averaged) into several groups of
KK subjects corresponding to the course curriculum. Meanwhile the target data is the selected KK for each
student having corresponding courses marks.
Table 6. Attribute of KK Selection dataset
Attribute
Compulsory subjects
ICM subjects
SIDE subjects
TELE subjects
Lab courses
Selected KK
Value
Real [0 .. 4]
Real [0 .. 4]
Real [0 .. 4]
Real [0 .. 4]
Real [0 .. 4]
ICM = 1, SIDE = 2, TELE = 3
The general process flow in the system is started with input data that has been previously pre-processed.
The data is the train set, which is a set of records used to build the classifier model. Next, the process goes to
run training phase, the process of forming and optimizing the model, so that a classifier model is obtained.
The trained model then be tested to see the performance or ability in classifying test data that had not been
processed before.
Here is a general view of the classification system development in this study.
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
START
Test
set
Train
set
19
Training using
ES algorithm
Testing
Classifier
model
Classification
results
FINISH
Figure 2. General overview of the classification system development using ES
The general form of the model classifier used in this study is a linear equation. Each input feature in the
data is multiplied by a weight, then the product of each pair of input and weight will be totaled. The set of
weight values is here said to be the classifier model. Results obtained by multiplying the number of inputs and
the weights will determine the level of eligibility to be classified to a particular class. The weights given for
one class are different with the weights given to other classes, but still with the same input. The output class is
determined by finding the highest value among these three values of eligibility.
The purpose of the model building process here is to find the right values for all weight multipliers to be
able to classify patterns of input data into classes in accordance with the best possible accuracy. Formulas (1)
to (4) show the classifier models used in this study.
{
(1)
(2)
(3)
(4)
where:
: eligibility to be classified to
: eligibility to be classified to
: eligibility to be classified to
: input values of the data
: weights for input 1 to to get the eligibility for
: weights for input 1 to to get the eligibility for
: weights for input 1 to to get the eligibility for
Figure 3 depicts the ES algorithm or scheme used in this study.
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
20
Mutation
Initiation
Population
Recombination
No
Termination?
New
Population
Survivor
Selection
Yes
End
Fitness
Mutated Chromosome + Offspring
Start
Decode &
Evaluation
Figure 3. Scheme or algorithm of ES
As described in the Literature Review section, here are some technical guides to perform ES algorithm.
1.
2.
3.
4.
Mutation process performed using the mutation step size. This explains that there is a limitation when
each individual will move or mutate from the original position. Thus, the evolutionary process becomes
more focused.
Recombination process has several choices of methods, namely Discrete or Intermediate in determining
the child genes, as well as Global or Local in the parent selection process.
ES has a selective pressure parameter that indicates one chromosome will be compared to a number of
chromosomes before being chosen as the best one and will survive in the next generation.
The process of recombination and mutation can be done in parallel, so the execution order is regardless.
Chromosomes that have been decoded was evaluated using the fitness formula which is defined as
follows.
(5)
Notes:
= the number of data records that is classified correctly
= the number of data records that is involved in training phase
In this study, a chromosome in ES represents the weighting multiplier values of each input feature data.
Input values on train set are multiplied by the weights to yield the eligibility value for admission to each class,
the class 1 to class n, where n is the number of classes on the data involved. By using the formula (1), the
output class will be obtained for each input pattern. Fitness value is obtained by calculating the percentage
level of accuracy between output and target class that has been given.
IV. RESULTS AND DISCUSSION
During the experiment, training phase through an evolution process and testing phase to see the
performance of the classifier model that had been trained, was conducted using the test set. The purpose of
this experiment was to analyze the influence of some parameter values on the evolutionary process and result.
In addition, the observations were also done to obtain optimal combination of the parameter values, including
population size, selective pressure, and recombination method.
For each experiment and observation, the specified maximum generation was 50 and it used ( , )selection as the survivor selection method. There were two conditions as the criteria of the evolution
termination. First, if it had met the predefined maximum generation and the second one was if the best fitness
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
21
did not change in a number of consecutive generations. Each observation was applied to 3 datasets that have
been prepared, the Fisher's Iris, SMK Major Election, and KK Selection.
As the information on each resulted table to be analyzed, scheme = chromosome scheme; popOrtu = the
size of the parent population; selPres = selective pressure; selOrtu = method of parent selection; hitGen =
how to calculate the child's genes; accTr = average accuracy rate of train set (%); accTs = average accuracy
rate of test set (%); and Wkt = average processing time (seconds).
A. Observing the Size of Parent Population
In the first stage of ES observation, there was no information related to the values of the parameters that
should be used. Therefore, the determined values were commonly set. The selective pressure was 7, while the
Global Discrete method was used in the recombination process.
Table 7. Observation results of the influence of parent population size to the system performance
Parameter
Scheme popOrtu
1
5
1
10
1
20
1
50
2
5
2
10
2
20
2
50
accTr
79.7
88.3
90.7
95.7
85
92.6
97.1
97.9
Iris
accTs
78.4
82.2
88.6
92.2
83.2
87.6
92
92.4
Wkt
0.8
2.27
3.52
11.9
0.86
2.07
5.36
13.3
SMK Major
accTr accTs Wkt
60.9
49.2 1.34
61.3
47
2.72
61.5
47.4
6.6
61.8
47.7 17.9
60.7
48.9 1.24
61.2
46.7 2.11
61.2
48.2
4.5
61.4
47.2 11.8
KK Selection
accTr accTs Wkt
71.9
69.8 2.28
74.8
72.3 4.49
75.8
78
9.65
75.1
74.3
21
66.8
66.6
1.7
70.4
69.8 4.78
78.8
75.8 16.1
81
77.6 42.9
The data in the table above is then simplified and resummed to obtain the average values for accuracy
rate and processing time resulted by given parent population size values. Accuracy level demonstrates the
ability of the model to classify the data, either on the train or test. Meanwhile, the processing time shows the
speed of the ES searching process to reach convergent condition. In that condition the best-so-far solution is
saturated or not changed anymore.
Table 8. The overall results from observation of parent population size
popOrtu
Acc (%)
Wkt (s)
5
68.4
1.37
10
71.2
3.08
20
74.6
7.62
50
75.4
19.8
Figure 4. Charts of the influence of the parent population to the ES performance for both the accuracy level and processing time
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
22
Based on the overall observation results table and chart above, it appears that in terms of accuracy, the
greater the parent population size are used, the ES searching process will produce a better solution models.
The size of the population describes the number of chromosomes that is evaluated by ES in every generation.
Among chromosomes in the population, the best chromosome is obtained for each generation. The larger the
population, the greater the chance of ES to get a better solution. In this experiment, it shows that the value of
50 produces the best accuracy rate. Although this rate is still very possible to go up if the population size is
increased, a value of 50 will be used as the size of the population in the next observation. It also considers that
the accuracy improvement of 20 to 50 is not too high, so as expected, if the size is increased, the accuracy
improvement would not be too big as well.
While in terms of processing time, it is clear that the larger the population size, the longer processing
time will be taken because of more chromosomes that must be evaluated. This is certainly something to be
’paid’ if the population size is increased. The computational cost is also be considered, so it is not required to
use more than 50.
B. Observation to the Selective Pressure
In the second stage of ES observation, the size of parent population used is 50, as the best result from
previous observation. Meanwhile, the Global Discrete was still used as default method in the recombination
process.
Table 9. Observation results of the influence of selective pressure to the system performance
Parameter
Scheme selPres
1
1
1
2
1
3
1
4
1
5
1
6
1
7
2
1
2
2
2
3
2
4
2
5
2
6
2
7
accTr
73.6
80.1
90.3
87.1
89.9
95.5
92.4
75.3
83.7
93.8
96.6
97.3
97.4
97
Iris
accTs
70
71
85.6
80.8
88
92.8
89
65.4
75.8
89.4
93.6
92.6
93.2
92.8
Wkt
1.93
3.21
4.01
5.83
7.34
9.64
8.77
2.22
4.08
5.34
6.88
10.7
11.5
12
SMK Major
accTr accTs Wkt
60.7
49.2 3.25
61
48.4
4.8
61.2
48.4 7.75
61.3
48.2 10.7
61.7
46.3 17.8
61.3
47.7 12.8
61.6
47.3 18.3
60.9
48.9 3.41
61.1
48.8 5.24
61.3
47.9 8.08
61.1
48.6 9.14
61.7
47.4
12
61.5
48.2 13.2
61.4
48.6 14.6
KK Selection
accTr accTs Wkt
66.1
66.3
7.7
69.3
68.4 12.8
71.9
73.1
18
74.2
74.1 20.8
75.6
75.4 29.7
74.2
73.9 24.5
77
75.4 37.6
64.1
62.9 7.41
67.9
66.6 12.7
73.2
72
16.3
77.5
76.9 27.9
78.2
74
29.4
78.1
77.4 45.8
80.6
79.7 41.6
The data in the table above is then simplified and resummed to obtain the average values for accuracy
rate and processing time resulted by given selective pressure values.
Table 10. The overall results from observation of selective pressure
selPres
Acc (%)
Wkt (s)
1
64
4.3
2
67
7.1
3
72
10
4
73
14
5
74
18
6
75
20
7
75
22
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
23
Figure 5. Charts of the influence of the selective pressure to the ES performance for both the accuracy level and processing time
Selective pressure can describe the number of chromosomes that must be countered by a particular
chromosome to be chosen as the best chromosome. For instance, if the selective pressure is set to 5, then for
every group that contains (5 + 1) chromosomes taken randomly, a chromosome will be chosen as the best one
to be maintained for the next generation. The amount of selective pressure on the ES will directly affect the
designated number of new chromosomes that are generated through mutation and recombination operation.
Similar to previous observations, in terms of the level of accuracy that is produced, with the increasing
number of new chromosomes are generated, the chance of ES to get better chromosomes is getting greater as
well. ES searching process is also becoming more exploratory with more and more widespread the candidate
solution is evaluated. In the first chart, it can be seen that when the value of selective pressure is increased
from 1 to 6, the accuracy rates of the resulted models are continued to rise. However, when it was closed to 7,
the resulted accuracy differences becomes not too far away, even almost the same. It means that the condition
at that point have already started converging, so if the value of the selective pressure continues to be added,
the accuracy may not be much different.
While on the other hand, the greater the value of selective pressure, the greater the computing time
required. It is already quite clear since with more new chromosomes that must be evaluated, ES needs longer
computational cost as well. With accuracy rates that is started to reach convergent condition, while processing
time will continue to be increased, so that 7 is chosen as the optimal selective pressure in this experiment and
will be used for the next observation.
C. Observation to the Recombination Method
This observation uses fixed values for several parameters obtained from previous observations. The
parent population size is 50 and the selective pressure is 7. These values are used in hopes of getting the best
result as well in this observation.
Table 11. Observation results of the influence of recombination method to the system performance
Scheme
1
1
1
1
2
2
2
2
Parameter
selOrtu hitGen
1
1
1
2
2
1
2
2
1
1
1
2
2
1
2
2
accTr
90.2
98.9
96.6
93.4
94.5
98.7
95.5
98.2
Iris
accTs
83.6
93.8
93.6
90.8
92
94.4
92.2
93.8
Wkt
7.47
10.2
9.57
10.2
11.3
10.8
10.1
13.2
SMK Major
accTr accTs Wkt
60.8
49.2 10.5
62.3
46.8 21.5
61.8
46.2 14.6
61.3
47.6
15
61.2
47.1 12.3
61.7
47.8 14.9
61.5
48.2 29.3
61.5
47.2 15.2
KK Selection
accTr accTs Wkt
66.1
64.7 14.3
87
84
42.3
77.6
76
21.9
74.9
75.4
25
72.9
70.2 22.8
80.2
77.9 29.6
74.8
73.7 20.4
84.5
80.5 37.1
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
24
The data in the table above is then simplified and resummed to obtain the average values for accuracy
rate and processing time resulted by given method combinations of parent selection and calculating child’s
genes.
Table 12. The overall results from observation of recombination method
selOrtu|hitGen
Acc (%)
Wkt (s)
11
71
4.74
12
77.8
8.33
21
74.8
13.1
22
75.8
19.9
Figure 6. Charts of the influence of the recombination method to the ES performance for both the accuracy level and processing time
Based on the overall observation results table and chart above, it shows that the computational cost of
searching process done by ES is very influenced by the recombination method used. It indicates that each
recombination method has its own algorithm complexity. On the second chart, it appears that the combination
of local intermediate method has the lowest complexity, while recombination with a combination of discrete
global method has the highest complexity.
By selecting the parent chromosomes locally, ES only needed to find a pair of chromosomes to produce
one new chromosome. While using global method, the pair of chromosomes to collect was as much as the
number of genes on the chromosome. Meanwhile, the process of calculating the intermediate genes was
carried only by calculating the mean between each pair of corresponding genes from both parent
chromosomes. This could be done in a single process count. In contrast to the discrete method, in which for
each pair of corresponding genes, ES had to choose which one would be taken for the child's gene. Thus, the
process would be repeated as many times as the number of genes.
On the other hand, in terms of accuracy, the combination of discrete local method showed the best result
among other combinations. By choosing parents locally, ES became more focused on the pair of
chromosomes. Thus, the searching space was smaller, which was just on the two chromosomes. Meanwhile
by the global method, the searching space was getting larger, which consisted of n pairs of parent
chromosomes. It would be more possibly to get a worse chromosome. Besides, good chromosomes basically
came from good parent chromosomes as well. However, this condition would be difficult to achieve if the
selection was done globally, where the child chromosomes were resulted by mix of many pairs of parents.
When a good chromosome was chosen as a parent, good genes from the chromosome will be ’damaged’ by
other worse chromosomes that are also selected as parents.
Ind. Journal on Computing Vol. 1, Issue. 2, Sept 2016
25
Meanwhile, calculations using discrete method (x|2) looks better than the intermediate (x|1). It can be
seen from the first chart that the combination of 1|2 is better than the 1|1 and 2|2 better than 2|1. Basically,
discrete method takes gene values that are already exist in the parent chromosomes. While the intermediate
method calculates parent’s genes to produce new genes with new values. So, a child generated by discrete
method is combination of values that exist in the parent chromosomes, whereas a child generated by
intermediate method always has new values.
Based on the processes that occur, intermediate method tends to be faster in achieving optimum points.
However, that is what makes the method getting more quickly and more likely to encounter premature
convergence because it is stuck in a local optimum conditions. Meanwhile, the discrete method relatively
longer to achieve optimum points. But, that feature makes ES avoids premature convergence in a local
optimum point, so that the results are truly the best. In addition, based on table 7, 9, and 11, it can be seen that
the results of the classification on Iris dataset is the most excellent among the three datasets were used. While
the SMK Major Election dataset is the most difficult to be classified. This is caused by the Iris dataset that is
linearly separable, so it will be easier to be classified by the basic model that belongs to linear classifier.
Table 13. Best accuracies of the models resulted by ES for the three datasets
Accuracy
Train (%)
Test (%)
Fisher’s Iris
98.9
94.4
SMK Major
62.3
49.2
KK Selection
87
84
The SMK Major Election dataset that produces the lowest accuracy showed that the data pattern is the
most non-linearly separable among the three datasets. It certainly makes the linear classifier model used in
this study getting difficult to classify the data pattern. Thus, the low accuracy rate resulted from the
experiment is not due to ES that is not capable of searching the solution, but the general classifier model that
is less able to cope with the complexity of a given problem. This can be resolved by using a non-linear
classification model in the next study.
V. CONCLUSION AND FUTURE WORK
Based on experiments that have been conducted, it can be concluded that ES is good enough in
optimizing the linear classifier model. ES has several unique attributes and features that are beneficial in the
searching process. In ES, the parameters of population size, selective pressure, and recombination method
used affect the results obtained from the evolutionary process, both in terms of the accuracy rate and the
processing time. Based on overall observations made, the optimal values for those three parameters are
respectively 50, 7, and discrete local. For Fisher's Iris dataset, the most easily to be classified, the best testing
accuracy rate achieved is 94.4%, while for KK Selection is 84%, and for SMK Major Election datasets as the
hardest to reach is 49.2%. Those different results occurred by influence of the linearity of the data distribution
as well as the data dimension. The more linear, the data is getting easier to be classified. Meanwhile, if the
size of the data is getting bigger, commonly it is more difficult to be classified.
As for development purposes of the future works, it is necessary to use a classifier model that is more
complex and can handle various conditions of data distribution, both linearly separable and non-linearly
separable. In addition, it can also be compared with other methods of Evolutionary Algorithms or Swarm
Intelligence based optimization method for the training phase.
ACKNOWLEDGMENT
The authors would like to thank the funding bodies of this research provided by Directorate of Research
and Community Service (DP2M), Telkom University, in The Internal Research Grant Program 2015.
Mahmud Dwi Sulistyo et.al.
Implementation of Evolution Strategies for...
26
REFERENCES
[1] Bäck, T., & Schwefel, H. P. (1993). An Overview of Evolutionary Algorithms for Parameter Optimization. Evolutionary Computation,
1(1), 1-23.
[2] Dianati, M., Song, I., & Treiber, M. (2002). An Introduction to Genetic Algorithms and Evolution Strategies. Technical report,
University of Waterloo, Ontario, N2L 3G1, Canada.
[3] Eiben, A. E., & Smith, J. E. (2003). Introduction to Evolutionary Computing. Springer Science & Business Media.
[4] Go, A., Bhayani, R., & Huang, L. (2009). Twitter Sentiment Classification Using Distant Supervision. CS224N Project Report,
Stanford, 1, 12.
[5] Gottlieb, J., Marchiori, E., & Rossi, C. (2002). Evolutionary Algorithms for the Satisfiability Problem. Evolutionary Computation,
10(1), 35-50.
[6] Greenwood, G. W., Gupta, A. K., & McSweeney, K. (1994, June). Scheduling Tasks in Multiprocessor Systems Using Evolutionary
Strategies. In International Conference on Evolutionary Computation (pp. 345-349).
[7] Hermawati, Fajar Astuti. (2013). Data Mining. Penerbit Andi.
[8] Jones, G. (1998). Genetic and Evolutionary Algorithms. Encyclopedia of Computational Chemistry.
[9] Louchet, J. (2000). Stereo Analysis Using Individual Evolution Strategy. In Pattern Recognition, 2000. Proceedings. 15th
International Conference on (Vol. 1, pp. 908-911). IEEE.
[10] Muhammad, L., Dayawati, R. N., & Rismala, R. (2014). Brain Tumor Detection and Classification In Magnetic Resonance Imaging
(MRI) using Region Growing, Fuzzy Symmetric Measure, and Artificial Neural Network and Connected Component Labeling.
International Journal on Information and Communication Technology| IJoICT, 1(1).
[11] Nguyen, Danh V., and David M. Rocke. "Tumor classification by partial least squares using microarray gene expression data."
Bioinformatics 18.1 (2002): 39-50.
[12] Oliveto, P. S., He, J., & Yao, X. (2007, September). Evolutionary Algorithms and the Vertex Cover Problem. In Evolutionary
Computation, 2007. CEC 2007. IEEE Congress on (pp. 1870-1877). IEEE.
[13] Ostertag, M., & Kiencke, U. (1995, September). Optimization of Airbag Release Algorithms Using Evolutionary Strategies. In
Control Applications, 1995., Proceedings of the 4th IEEE Conference on (pp. 275-280). IEEE.
[14] Pennacchiotti, M., & Popescu, A. M. (2011). A Machine Learning Approach to Twitter User Classification. ICWSM, 11, 281-288.
[15] Ragab, A. H. M., Noaman, A. Y., Al-Ghamdi, A. S., & Madbouly, A. I. (2014, June). A Comparative Analysis of Classification
Algorithms for Students College Enrollment Approval Using Data Mining. In Proceedings of the 2014 Workshop on Interaction Design
in Educational Environments (p. 106). ACM.
[16] Rismala, R. (2015). Prediksi Time Series Tingkat Inflasi Indonesia Menggunakan Evolution Strategies. Jurnal Ilmiah Teknologi
Informasi Terapan, 1(2).
[17] Sulistiyo, Mahmud Dwi, Dayawati, R. N., Nurlasmaya. (2013, November). Evolution Strategies for Weight Optimization of Artificial
Neural Network in Time Series Prediction. In Robotics, Biomimetics, and Intelligent Computational Systems (ROBIONETICS), 2013
IEEE International Conference on (pp. 143-147). IEEE.
[18] Suyanto, ST., MSc. (2008). Evolutionary Computation: Komputasi Berbasis “Evolusi” dan “Genetika”. Informatika.
[19] Tsai, H. K., Yang, J. M., Tsai, Y. F., & Kao, C. Y. (2004). An Evolutionary Algorithm for Large Traveling Salesman Problems.
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 34(4), 1718-1729.